Method and apparatus for rotary actuator arc compensation correction in a direct access storage device

ABSTRACT

Rotary actuator arc compensation correction method and apparatus are provided for a direct access storage device (DASD). A reference feedforward correction signal is generated at each of a plurality of sectors around a predetermined track on a disk surface. A specific selected track is identified, and both magnitude and phase of the generated reference feedforward correction signal are modified to correct for the arced trajectory caused by the rotary actuator at the specific selected track. Improved actuator servo control is provided by using pseudo sector compensation to interpolate the feedforward correction signal between servo sectors.

This application is a continuation of application Ser. No. 08/112,408,filed Aug. 26, 1993 now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to a method and apparatus for rotaryactuator arc compensation correction in a direct access storage device(DASD).

2. Description of the Prior Art

Computers often include auxiliary memory storage units having media onwhich data can be written and from which data can be read for later use.Disk drive units incorporating stacked, commonly rotated rigid magneticdisks are used for storage of data in magnetic form on the disksurfaces. Data is recorded in concentric, radially spaced datainformation tracks arrayed on the surfaces of the disks. Transducerheads driven in a path toward and away from the drive axis write data tothe disks and read data from the disks.

All DASD units must have a method to position each data head over theproper radial location to write a track and again, to position it veryclose to the same location to read the track. With the higher levelfiles using a voice coil type of actuator, a feedback mechanism must beprovided to locate and stably hold the head on a given track. Typically,track accessing and track following is provided utilizing a magneticallywritten pattern in the DASD unit. A dedicated servo system employs onesurface of one of the disks in the DASD on which to have all thetracking and access information. A sector servo system uses smallportions of tracks between each or between several sectors on each trackof each data surface to provide the tracking and access information. Ahybrid servo system uses both to obtain advantages of each type ofservo.

The degree of tracking accuracy, i.e., the ability of the actuator servoto keep the head position discretely over the track, is governed by twofactors. One factor is spacial (space), the other is temporal (time).The spacial factor corresponds to the number of servo sectors N aroundthe track, which is a function of the linear recording density and thefixed block data format. The temporal factor corresponds to the timebetween servo sectors or the sampling period, which is controlled by therotational disk velocity (RPM).

Track misregistration (TMR) error can be separated into two majorcomponents, repeatable or synchronous with disk rotation andnon-repeatable or asynchronous with disk rotation. The repeatable TMRcomponent, which can be large in case of a disk slip, can be reduced bycorrection compensation. A correction for radial track misregistration(TMR) versus radius is required for a DASD with a rotary actuator whentracks are written approximately uniformly on the rotary arc rather thanin the radial direction. Both the gain and phase effects with radiusshould be compensated. Both gain and phase effects with radius producecomparable amounts of TMR error in the system.

In DASD with a rotary actuator, the head does not move in a radialdirection. For many disk drives, the skew angle of the head has the backend of the head further out on the disk than the front when the head isat the inner radius. The skew gets progressively larger at larger radii.This is used to advantage in the drives by writing the tracks nearlyuniformly on the arc that the head transverses from the inner radius tothe outer radius. Due to the larger skew angles, the written tracks arephysically smaller near the outer radius than near the inner radius. Thepositioning of the tracks on the arc causes the radial track pitch to besmaller at the outer radii than at inner radii, which is consistent withthe smaller written tracks.

A radial movement of a disk, such as that due to disk slip, or othervibrations producing an apparent out-of-round for the track, moves thedisk the same physical distance at any radius. However, in the servosystem, the distance is measured in fractions of a pitch. Typically thisdistance is in 1/512 of a customer track pitch. Since the head is movedat the skew angle for a given radius, the head must be moved furtherthan the radial movement of the disk, and this amount is moresignificant at the outer radii where the skew angle is larger than atinner radii.

As a result, any compensation for radial TMR that is determined at oneradius in a given number of units in the servo system will not be thesame value at other radii. For example, a difference between the outsidediameter (OD) and the inside diameter (ID) can be about 7%. Atprogressively higher track density this has some significance as anerror in the corrections. Also, when a prewritten servo disk is used,there can be significant repeatable runout, thus increasing themagnitude of the error.

In known disk files which used dedicated servo control, it was necessaryto add a reference profile to correct for runout due to disk slip orrelative thermal motion between each head and the corresponding trackson the data surface. These reference profiles, measured for each datasurface, would have been correct if a linear actuator was used, since alinear actuator will normally follow a radial trajectory on a disk. Onthe other hand, a rotary actuator follows an arc rather than a radialline on the disk, thus there will be a phase error between the trackwhere the runout was measured and any other track.

Known feedforward or profile compensation techniques used for rotaryactuators to correct for runout or disk slip have a systematic error,for example, such as, up to 10% of the runout for 3.5" DASD caused bythe arc made by the product head. A disk slip and/or imbalance willoccur in a radial direction, and not along the head arc, thus themeasured profile will only be correct at the track or cylinder ofmeasurement. All other tracks will have an incorrect profile for optimalrunout compensation.

SUMMARY OF THE INVENTION

Important objects of the present invention are to provide a method andapparatus for rotary actuator arc compensation correction in a directaccess storage device; to provide such method and apparatus thatcompensates for a small predefined number of servo sectors around arevolution of a disk; and to provide such method and apparatussubstantially without negative effects and that overcome many of thedisadvantages of prior art arrangements.

In brief, the objects and advantages of the present invention areachieved by a method and apparatus for providing rotary actuator arccompensation correction in a direct access storage device (DASD). Areference feedforward correction signal is generated at each of aplurality of sectors around a predetermined track on a disk surface. Aspecific selected track is identified, and both magnitude and phase ofthe generated reference feedforward correction signal are modified tocorrect for the arced trajectory caused by the rotary actuator at thespecific selected track.

In accordance with another feature of the invention, an improvedactuator servo control is provided by using pseudo sector compensationto interpolate the feedforward correction signal between physical servosectors.

BRIEF DESCRIPTION OF THE DRAWING

The present invention together with the above and other objects andadvantages may best be understood from the following detaileddescription of the embodiments of the invention illustrated in thedrawings, wherein:

FIG. 1 is a schematic and block diagram of a data storage disk fileembodying the present invention;

FIG. 2 is a diagram showing the accessing mechanism for a single disksurface of the apparatus of FIG. 1;

FIG. 3 is a diagram illustrating apparatus for carrying out the rotaryarc compensation correction methods according to the present inventionin the data storage disk file of FIG. 1;

FIG. 4 is a chart illustrating feedforward correction angles relative tological track addresses;

FIG. 5 is a chart illustrating normalized runout amplitude relative tosector index n at the inside diameter (ID) and at the outside diameter(OD) shown in dotted line;

FIG. 6 is a chart illustrating normalized runout error due to phaseshift between the inside diameter (ID) and the outside diameter (OD)relative to sector index n; and

FIG. 7 is a chart illustrating simulated runout correction relative topseudo sector index m.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In FIG. 1 there is shown a partly schematic block diagram of parts of adata storage disk file 10 including a data storage medium generallydesignated as 12 and a control unit generally designated as 14. In thepreferred embodiment of this invention, the data storage medium 12 isembodied in a rigid magnetic disk drive unit 12, although othermechanically moving memory configurations may be used. Unit 12 isillustrated in simplified form sufficient for an understanding of thepresent invention because the utility of the present invention is notlimited to the details of a particular drive unit construction.

Referring now to FIGS. 1 and 2 of the drawings, disk drive unit 12includes a stack 16 of disks 18 having at least one magnetic surface 20.The disks 18 are mounted in parallel for simultaneous rotation on and byan integrated spindle and motor assembly 26. Data information on eachdisk 18 are read from and/or written to by a corresponding transducerhead 28 movable across the disk surface 20.

Transducer heads 28 are mounted on flexure springs 30 carried by arms 32ganged together for simultaneous pivotal movement about a supportspindle 34. One of the arms 32 includes an extension 36 driven in apivotal motion by a head drive motor 38. Although several drivearrangements are commonly used, the motor 38 can include a voice coilmotor 40 cooperating with a magnet and core assembly (not seen)operatively controlled for moving the transducer heads 28 in synchronismin a radial direction in order to position the heads in registrationwith data information tracks or data cylinders 42 to be followed andaccess particular data sectors 44. Data storage disk file 10 is amodular unit including an enclosure or housing 46. The variouscomponents of the disk file 10 are controlled in operation by signalsgenerated by control unit 14 such as motor control signals on line 26Aand position control signals on line 38A.

Numerous data information tracks 42, each at a specific radial location,are arrayed in a concentric pattern in the magnetic medium of each disksurface 20 of data disks 18. A data cylinder includes a set ofcorresponding data information tracks 42 for the data surfaces 20 in thedata storage disk file 10. Data information tracks 42 include aplurality of segments or data sectors 44, each for containing apredefined size of individual groups of data records which are saved forlater retrieval and updates. The data information tracks 42 are disposedat predetermined positions relative to a servo reference index. In FIG.2 one sector 44 is illustrated as SECTOR 0 with a fixed index or markINDEX for properly locating the first data sector. The location of eachnext sector 44 is identified by a sector identification pulse (SID) readby transducer heads 28 from surfaces 20.

In accordance with the invention, systematic error can be effectivelyeliminated for each individual track using a very simple algorithm toyield optimal tracking performance for each individual data surface. Themethod simply modifies the Fourier coefficients as functions of thetrack position to obtain the correct runout compensation for a specifictrack before the inverse Fourier transform is taken.

Referring now to FIG. 3 there is shown a block diagram illustratingrotary arc compensation correction apparatus generally designated 50. Aservo processor 52 provides a control signal to a digital-to-analogconverter (DAC) 54 coupled to a current driver 56. Current driver 56provides a control current to a rotary actuator 58 for moving thetransducer heads 28 of a R/W channel 60. Detected position dataindicated at a block 62 is coupled to the servo processor 52.Feedforward control block 64, coupled to the servo processor 52,provides control information for both magnitude and phase compensationcorrection versus track number or change in radius and for pseudo sectorcorrection compensation. For proper compensation of feedforward signalsto the file, both the magnitude and phase of the correction must becompensated versus the track number or change in radius.

Referring to FIG. 2, the angle α(r) defined by A-O-X, where X is theintersection between a circle of radius r centered at 0 and the arc B-Ccan conveniently be found from the Law of Cosines. This angle isreferred to as α(r).

The cosine to α(r) is given in Equation 1 below: ##EQU1##

The cosine to the angle α(R_(o)) is found by substitution of r=R_(o) inEquation 1 above, giving: ##EQU2##

It can be shown that the difference angle θ(r) between α(r) and α(R_(o))can be approximated by the simple algorithm derived from simulations:##EQU3##

Let L be an arbitrary logical cylinder number corresponding to acylinder of radius r, and let L_(o) be the total number of cylinders inthe data band defined by (R_(o) --R_(i)). Furthermore, let L be equal tozero for r=R_(o), and L=L_(o) for r=R_(i). It is now possible to expressEquation 3 in terms of m as ##EQU4## where coefficients K₁, K₂ and K₃are given by ##EQU5## and finally ##EQU6## For a certain 3.5" drive withR_(a) =52 mm, R_(b) =57 mm, R_(o) =45.52 mm, Ri=20.68 mm, and at a trackdensity of 3300 tpi, the total number of data tracks L_(o) =3227. Thevalues for the K's are K₁ =7.603×10⁻⁵, K₂ =1555.4 and K₃ =5913.6. Thecorresponding angles α(R_(o)) and α(R_(i)) are 59.71° and 65.63°,respectively. The difference angle at the inner cylinder, i.e., cylinder3227, using the approximation formula in Equation 4 yieldsθ(L_(o))=5.9189° compared to the correct value of 5.9195°. Thiscorresponds to a maximum error of about 0.01%.

Nonlinear phase error is only a function of the hard disk drive geometryas illustrated in FIG. 2. It is therefore a predictable and systematicerror and can be calculated within a very small margin for any logicalcylinder L using Equation 4.

Assume for example that the runout is measured for each of N sectors atthe outer track (OD) and let us designate the measured by x(n), where nis an integer n=0, 1, . . . , N-1. Furthermore, assume that the firstharmonic runout component x₁ (n) is extracted from the OD measurementx(n). This can easily be done by Fourier Harmonic Filtering. Let theDiscrete Fourier Transform (DFT) of x(n) be

    X(k)=A(k)+jB(k)                                            (8)

where A(k) and B(k) are the real and imaginary Fourier coefficients,respectively. The index k takes on integer values k=0, 1, . . . , N-1.

Considering that the fundamental runout component x₁ (n) corresponds tok=1, then it can shown that ##EQU7## where A(1) and B(1) are given by##EQU8##

It can be shown that for θ(L)<<1 radian, which is the case here, thatthe phase corrected feed-forward compensated first harmonic runoutsignal x₁ (n,L) can be approximated by the equation ##EQU9## where thefirst harmonic phase corrected Fourier coefficients for cylinder (track)L C(1,L) and D(1,L) are

    C(n,L)=A(1)+θ(L) B(1)                                (13)

    D(n,L)=B(1)-θ(L) A(1)                                (14)

The first harmonic phase corrected Fourier co-efficients C(1,L) andD(1,L) in Equations 13 and 14 are easily calculated from Equations 4, 10and 11.

Application of the phase corrected feedforward runout signal x(n,L) inEquation 12 for an arbitrary cylinder L will optimize the feedforwardcompensation and reduce the systematic error to near zero.

In accordance with another feature of the invention, a simple quadraticcorrection for amplitude corrected feedforward compensation as followscan provide excellent fit to the actual curve, making an assumption thatthe angles are small and the curve fit is for a small range. First, theradial pitch equals the pitch on the arc multiplied by the cosine of theskew angle. The cosine is the square root of 1-sine². The sine of theskew angle is approximately the skew angle in radians. The skew anglecan be approximated by using an offset and an amount proportional to aradial distance. Then, even though the track pitch varies somewhat, aradial distance is related approximately linearly to a number ofcylinders.

Now, let Nc=logical cylinder number, where Nc=0 on the outer track, andNc=4118 on the inner track. Also, for reference, Nc=3002 at the switchradius where the skew angle is 11.27 degrees.

With the previous approximations, the cosine of the skew angle isapproximated as:

    cos(skew)=1-((N1-Nc)/N2).sup.2                             (15)

where N1 is the offset, and N2 is a scaling constant.

For Nc=0 at SKEW=22.36 degrees

Nc=4118 at SKEW=6.57 degrees

Then N1=5831, and N2=21144

Then using:

Pitch(approx)=6.23 um (1-((N1-Nc)/N2)² and comparing to actual values wehave:

    ______________________________________                                        RADIAL POSITION                                                                             ACTUAL RAD. PITCH                                                                            PITCH (approx)                                   ______________________________________                                        Inner Radius 20.68 mm                                                                       6.19 um        6.19 um                                          Switch Point 27.50 mm                                                                       6.11 um        6.12 um                                          Outer Radius 45.52 mm                                                                       5.76 um        5.76 um                                          ______________________________________                                    

Note that for a given radial distance of repeatable runout, the numberof servo counts is inversely proportional to the radial pitch.

If RRO counts are measured at track zero (at R_(o) in FIG. 2), then theRRO counts at another cylinder are defined as follows: ##EQU10##

If desired, the factor on the right can be further simplified by theseries for the reciprocal, using only up to the second order term in thenumerator. Also, moderate improvement is provided using only up to thelinear term in the series.

Following is a Table 1 listing a more complete calculation of the effectof a uniform track density on the arc, which generates a nonlinearvariation with radius. The ACTUATOR ANGLE in degrees is the angle fromthe actuator axis to disk axis line, and to the actuator axis to thehead gap line. For this example, the distance from the actuator axis todisk axis is 56.50 mm. The distance from actuator axis to gap is 55.00mm. These distances along with the radius describe a triangle, and theLaw of Cosine relates the angles to the sides. The distance along thearc is assumed to be linearly proportional to the track number. Theinner track radius, outer track radius and number of tracks defines thetrack pitch on the arc. This geometry is also used to calculate thecircumferential phase error. This was taken with the zero reference attrack zero, which is at the outer data radius. The phase error is thechange in the radial line to the head gap compared to the line with thehead at the outer track.

The CORRECTION-ACTUAL column is the reciprocal of the COSINE of the headskew angle. This is the factor applied to the servo counts to move thesame distance compared to the straight radial distance. If a measurementis taken at one radius, the amount to move at a second radius can beobtained by dividing by the factor for the first radius and multiplyingby the factor for the second radius.

The CORRECTION-APPROX is a quadratic approximation of the correctionfrom the previous column, fitting the 000 track, the 4134 inner track,and the 2067 middle track. There is a 7.4% difference between the innerand outer values, so a fixed fraction of a track runout correction wouldlead to a 7.4% error on the opposite end of the band. Note that thesimple quadratic fit has a very small maximum error of 0.00019.

However, even if the radial magnitude of a correction is perfect, itwill not have the right result if it is not applied at the correct phaseangle of the disk's rotation. Note in table 1 that the PHASE ERROR has arange of 11.05 degrees. If a perfect correction for the inner track wereapplied with the phase from the outer track, there would be a residualerror of 19% of the correction.

The last column shows a quadratic approximation of the phase error. Theselection of coefficients here left a maximum error of 0.15 degrees.With this correction, the residual maximum error would be about the sineof this angle, or 0.0026 or about 1/4%.

This calculation was obtained assuming the track density was perfectlyuniform on the arc. This is a fair approximation. However, providingsome variation of track density on the arc allows packing the tracks alittle more tightly where there is better performance, thereby obtaininga little more capacity. In general, the center of the band can be packed2 or 3 percent more than the ends and then applied in an approximatequadratic variation. Although the following table 1 does not take thiseffect into account, it would only require a slight change in thecoefficients to include it. Thus we could also compensate for this addedvariation.

                                      TABLE 1                                     __________________________________________________________________________         ACTUATOR                      PHASE                                                                              PHASE                                 TRACK                                                                              ANGLE   RADIUS                                                                              CORRECTION                                                                            CORRECTION                                                                            ERROR                                                                              ERROR                                 N    deg     mm    ACTUAL  APPROX  (deg)                                                                              APPROX                                __________________________________________________________________________     000 48.17   45.52 1.0813  1.0813  0.00 0.00                                   200 46.87   44.37 1.0760  1.0760  0.59 0.59                                   400 45.57   43.20 1.0708  1.0709  1.19 1.18                                   600 44.28   42.04 1.0658  1.0660  1.78 1.76                                   800 42.94   40.87 1.0611  1.0612  2.36 2.33                                  1000 41.68   39.69 1.0565  1.0566  2.94 2.90                                  1200 40.38   38.51 1.0520  1.0522  3.52 3.47                                  1400 39.08   37.32 1.0478  1.0480  4.10 4.02                                  1600 37.79   36.13 1.0437  1.0439  4.66 4.58                                  1800 36.49   34.94 1.0398  1.0400  5.23 5.12                                  2000 35.19   33.74 1.0361  1.0362  5.78 5.67                                  2200 33.89   32.53 1.0325  1.0326  6.33 6.20                                  2400 32.59   31.32 1.0291  1.0292  6.88 6.73                                  2600 31.30   30.11 1.0259  1.0260  7.41 7.26                                  2800 30.00   28.89 1.0228  1.0229  7.93 7.78                                  3000 28.70   27.67 1.0199  1.0200  8.45 8.29                                  3200 27.40   26.45 1.0172  1.0172  8.95 8.80                                  3400 26.10   25.22 1.0146  1.0146  9.44 9.30                                  3600 24.81   23.99 1.0122  1.0122  9.90 9.80                                  3800 23.51   22.76 1.0100  1.0100  10.36                                                                              10.29                                 4000 22.21   21.53 1.0079  1.0079  10.78                                                                              10.78                                 4134 21.34   20.70 1.0066  1.0066  11.05                                                                              11.10                                 __________________________________________________________________________

FIG. 4 is a chart illustrating feedforward correction angles relative tological track addresses, taking for an example a 3.5" drive with Ra=52mm, Rb=57 mm, Ro=45.52 mm, R_(i) =20.68 mm, and at a track density of3300 tpi. FIG. 4 shows the required magnitude of the required correctionangle θ(L) as a function of the logical track address L. It can be seenthat the maximum error occurs at L-2900. Note that the phase error isnon-linear; and therefore, it is more complicated to provide phasecompensation correction.

FIG. 5 is a chart illustrating normalized runout amplitude relative tosector index n at the inside diameter (ID) and at the outside diameter(OD) shown in dotted line. Seventy-six servo sectors are assumed forthis example and in FIG. 6. In terms of the first harmonic runoutmeasured for the servo sectors at the outer track radius R_(o) and theinner track radius R_(i), there is a leading phase shift of 5.9° asmeasured at the inner track radius. This phase shift is clearly evidentin FIG. 5, which shows normalized runout amplitudes at the extremecylinders. The difference between the runout amplitudes in FIG. 5 isshown in FIG. 6.

FIG. 6 is a chart illustrating normalized runout error due to phaseshift between the inside diameter (ID) and the outside diameter (OD)relative to sector index n. This is the normalized feedforward errorbetween inner and outer tracks. It can be seen from FIG. 6 that thiserror is about 10% of the runout amplitude in FIG. 5.

In accordance with another feature of the invention, much betteractuator servo control and improved TMR is provided by interpolatingbetween a sparse number of servo sectors to yield many more feedforwardoutputs. Typically there are 60-90 servo sectors per track. For a givenlinear density and data blocking format, the number of servo sectors pertrack decreases linearly with decreasing form factors (FF). This can beseen from Table 2 below.

                  TABLE 2                                                         ______________________________________                                        Servo Sector Number for Small FF DASD                                         at Fixed Linear Density                                                       FORM FACTOR    SERVO SECTORS n                                                ______________________________________                                        3.5"           76                                                             2.5"           54                                                             1.8"           39                                                             1.3"           28                                                             1.0"           21                                                             ______________________________________                                    

While usually a smaller 1.0" drive spins much faster than a 3.5" driveto keep the recording heads flying, 21 sectors per track providesinadequate spacial resolution to maintain good tracking at high trackdensities. Thus, the method of the invention provides more spatialresolution without increasing the servo sector overhead on the disksurface.

First consider where w_(o), the discrete frequency for N servo sectorsis expressed as ##EQU11## The cos w_(o) n and sin w_(o) n, used in theabove Equations 12, 13, and 14 are generated by a simple code in theservo microprocessor 52. Note that Equations 10 and 11 are only updatedduring periodic measurements that may be a function of the ambientconditions, while Equation 12 is being used continuously.

Assume now that we modify Equation 12 by changing the discrete frequencyw_(o) to a lower discrete frequency w₁. Let this frequency be ##EQU12##where M is the number of virtual or pseudo sectors (M>N). Let m be thepseudo sector index such that 0<m<M-1 so that Equation 12 can bemodified to yield the estimated fundamental feedforward compensation.##EQU13##

If M=P×N where P is an integer, then there will be (P-1) pseudocorrection samples generated by Equation 19 between each of the Nphysical servo sectors.

Referring to FIG. 7, there is shown an arbitrary normalized runoutcorrection for a hypothetical 1.0" form factor DASD with N=21 sectorsindicated by squares and M=63 pseudo sectors (P=3) indicated byasterisks. If the 1.0" file only compensated for repeatable runout forevery physical servo sector (see squares) then the correction signalwhich is generated by a zero-order-hold (ZOH) or the digital-to-analogconverter (DAC) 54 would be rather coarse around the zero crossings ofthe sine wave. The pseudo sector compensation (see asterisks) providesmuch better resolution. The increased resolution provides a smoothercontrol signal for the actuator 58 and thus reduces the excitation ofactuator and suspension resonances. This would be the case for seek,settle, and track follow operational modes.

The number of pseudo sectors M is arbitrary and can be considered to bevariable. For example, during data recovery procedures (DRP) the numberof pseudo sectors M can be increased to provide better tracking. Thephase corrected feedforward compensation as given by Equation 19advantageously can be implemented in a separate module for completefreedom in the selection of M. This will minimize the impact on theregular actuator servo code.

It should be understood that this method can be used to reduce thenumber of physical servo sectors on larger form factor drives to yieldmore disk real estate for customer data. This would be the case fordrives that have larger repeatable TMR components compared tonon-repeatable TMR.

In brief summary, features of the invention include: Phase correction isprovided for feedforward runout compensation due to recording headsarced trajectory caused by rotary actuator. Amplitude or magnitudecorrection also is provided for feedforward runout compensation. Usingpseudo sector compensation by measuring runout using N physical sectorsand estimating runout compensation for M pseudo sectors per track persurface where M>N yields a smoother feedforward control and enablesimproved TMR and higher track densities. Only two RAM locations for eachhead are required for periodic updating of algorithms, i.e., A(1) andB(1), Equations 10 and 11. Rotary arc compensation correction can beutilized in various known feedforward compensation arrangements usedwith rotary actuators, e.g., an iterative feedforward method. Theefficient non-linear correction algorithms enable a micro-codeimplementation. Rotary arc compensation correction can be used for allservo methods used with rotary actuators, e.g., dedicated servo, hybridor dedicated plus reference track servo and sector servo. Also, existingdisk files can be retrofitted by a simple micro-code change to takeadvantage of the tracking improvements.

While the invention has been described with reference to details of theillustrated embodiment, these details are not intended to limit thescope of the invention as defined in the appended claims.

What is claimed and desired to be secured by letters patent of theunited states is:
 1. Apparatus for providing a feedforward correctionsignal to drive mechanism of a rotatable actuator in a disk storagedevice, comprising:means for generating a reference feedforwardcorrection signal at each of a plurality of sectors around apredetermined track on a disk surface, said reference feedforwardcorrection signal varying periodically as a function of angular positionof the disk, said means for generating a reference feedforwardcorrection signal includes means for measuring a runout error at each ofsaid plurality of sectors around said predetermined track; means foridentifying a specific selected track; means for calculating the changein the radial line to a transducer head at said specific selected trackcompared to the radial line with the transducer head at thepredetermined reference track; and means responsive to said identifiedspecific selected track and to said change in radial line for modifyingboth magnitude and phase of said generated reference feedforwardcorrection signal including means for calculating: ##EQU14## where thefirst harmonic phase corrected Fourier coefficients for track L C(1,L)and D(1,L) are

    C(1,L)=A(1)+θ(L)B(1)

    D(1,L)=B(1)-θ(L)A(1)

where A(1) and B(1) are real and imaginary Fourier coefficients for saidmeasured runout error and θ(L) is a difference angle between atransducer head angle at the predetermined track on a disk surface andat the specific selected track.
 2. Apparatus as recited in claim 1further includes means for calculating: ##EQU15## where M=P×N, where Pis an integer for generating (P-1) pseudo correction samples betweeneach of the N physical servo sectors around the track on the disksurface.
 3. Apparatus as recited in claim 1 further includes means forstoring A(1) and B(1) values for each transducer head in the diskstorage device.
 4. A method for providing a feedforward correctionsignal to a drive mechanism of a rotatable actuator in a disk storagedevice, comprising the steps of:generating a reference feedforwardcorrection signal at each of a plurality of sectors around apredetermined reference track on a disk surface, said referencefeedforward correction signal varying periodically as a function ofangular position of the disk; said step of generating a referencefeedforward correction signal at each of a plurality of sectors around apredetermined reference track on a disk surface includes the substep ofmeasuring a runout error at each of said plurality of sectors aroundsaid predetermined reference track; identifying a specific selectedtrack; means for calculating the change in the radial line to atransducer head at said specific selected track compared to the radialline with the transducer head at the predetermined reference track;modifying both magnitude and phase of said generated referencefeedforward correction signal responsive to said identified specificselected track and said change in radial line; said step of modifyingboth magnitude and phase of said generated reference feedforwardcorrection signal includes the substep of calculating: ##EQU16## wherethe first harmonic phase corrected Fourier coefficients for track LC(1,L) and D(1,L) are

    C(1,L)=A(1)+θ(L)B(1)

    D(1,L)=B(1)-θ(L)A(1)

where A(1) and B(1) are real and imaginary Fourier coefficients for saidmeasured runout error and θ(L) is a difference angle between atransducer head angle at the predetermined reference track on a disksurface and at the specific selected track.
 5. A method as recited inclaim 4 wherein said step of modifying both magnitude and phase of saidgenerated reference feedforward correction signal further includes thesubstep of calculating: ##EQU17## where M=P×N, where P is an integer forgenerating (P-1) pseudo correction samples between each of the Nphysical servo sectors around the track on the disk surface.